Global Warming &
Climate Sensitivity:
Climate Feedbacks in the Tropics
Professor Dennis L. Hartmann
Department of Atmospheric Sciences
University of Washington
Seattle, Washington
Berkeley Atmospheric Sciences Symposium
November 8, 2002
U.C. Berkeley
Two approaches to understanding
climate change.
• Top Down Approach - Take observed climate
record and attempt to extrapolate intelligently
into the future.
• Bottom Up Approach - Attempt to understand
and model the critical climate processes,
then use the resulting detailed model to predict
how future climates might respond to specified
forcing like CO2 increase.
Greenhouse gas trends
are large and can be
associated directly with
human actions.
Carbon dioxide trends
Can be uniquely associated
with fossil fuel burning
through isotopes of carbon
like 14C and 13C.
The Instrumental Record of Global
Temperature Anomalies.
IPCC - 2001
Model of Global Temperature Anomalies through time.
Energy Equation:
T
1
Q  C

T
t

Climate =
Forcing
Heat +
Storage
Heat
Loss
In Equilibrium, temperature is constant with time and so,
T   Q
 is a measure of climate sensitivity;
˚K per Wm-2 of climate forcing
To Project future climates by
using the observed record of
climate over the past century,
we need to know three things
to interpret the temperature
time series:
T
1
Q  C

T
t

Climate Forcing = Q (Wm-2)
Heat capacity = C (J oK-1 m -2)
Climate sensitivity =  (oK per Wm-2)
Heat Storage: Mostly the Oceans
1955-1996; Levitus et al. 2001: Science
World Ocean = 18.2 x1022 Joules
Atmosphere = 0.7 x1022 Joules
Land Ice
= 0.8 x1022 Joules
Model observed
Modeled
Model includes forcing from Greenhouse Gases, Sulfate Aerosols
Solar irradiance changes, and volcanic aerosols.
Model minus solar irradiance changes
and volcanic aerosols.
Top-Down Approach:
Determine sensitivity of climate
from observed record over past
130 years. Use simple model
to extrapolate into future.
Problems: Need to know:
• Climate forcing - uncertain, especially solar and aerosol forcing.
• Heat storage - somewhat uncertain.
• Climate sensitivity - also uncertain.
No two of these are known with enough precision to usefully constrain
uncertainty in the third, with the data available, although it is possible
to fit the observations with fair precision using even a simple model.
IPCC 2001
1850-2000 ~0.6oC Warming; 0.4oC per century
2000-2030 ~0.6oC Warming; 2.0oC per century*
*mostly warming from CO2 already in atmosphere
IPCC - 2001
Predictions for the year 2100
Between 1990 and 2100 global mean surface temperature
will increase by
1.4oC < T < 5.8oC
This large range of uncertainty arises in equal measure
from two principle sources:
• Uncertainty about how much climate forcing humans
will do, principally through fossil fuel consumption.
(Depends on political decisions, economic events,
technical innovation and diffusion.)
• Uncertainty about how the climate system will respond
to climate forcing by humans - Climate Sensitivity.
(Depends on natural processes.)
Bottom-up approach
Understand and model key
physical processes that affect
climate sensitivity.
i.e. Feedback Processes
• Water vapor feedback
• Cloud feedback
• Ice-albedo feedback
• Many more
Water Vapor Feedback:
• Water vapor is the most important greenhouse gas
controlling the relationship between surface temperature
and infrared energy emitted from Earth.
• Saturation vapor pressure increases about 20% for each
1% change in temperature (3 oC). 80
Saturation Vapor Pressure (hPa)
• Therefore, assuming that the
relative humidity remains
about constant, the strength
of the greenhouse effect will
increase with surface temperature.
70
Saturation Vapor Pressure (hPa)
60
50
40
30
20
10
0
-30
-20
-10
0
10
20
Temperature (ÞC)
30
40
Infrared Greenhouse
Effect:
The amount by which
the atmospheric reduces
the longwave emission
from Earth.
Greenhouse effect = Surface infrared emission - Earth infrared emission
155 Wm-2
=
390 Wm-2
-
235 Wm-2
Greenhouse effect = Surface longwave emission - Earth emission
Greenhouse Effect  Ts4  Earth Emission
To a first approximation,
the clear-sky greenhouse
effect is proportional to
the surface temperature.
Sea Surface Temperature
Sea Surface Temperature
And the Greenhouse Effect
is related to the amount of
water vapor.
Upper Troposphere Water Vapor
Mount Pinatubo Eruption
As a test of Water Vapor Feedback
Soden, et al., Science, 26 April 2002
Philippines
June 1991
Observed and Simulated Water Vapor
Testing
Water
Vapor
Feedback
Year
Observed and Simulated Temperature
Soden, et al., Science, 2002
Why is fixed relative humidity a good
approximation during climate change?
• The relative humidity RH is required to be between 0 and 1.
• The mass of air moving upward (RH ~1),
must be equal to the mass of air moving downward (RH~0+)
• The RH in the free atmosphere should be about 0.5
• The inadequacies in this theory for relative humidity
do not change that rapidly with climate, compared to
the saturation vapor pressure dependence on temperature.
Water Vapor Feedback
Effect on long-term response to doubled CO2
T   Q
 is a measure of climate sensitivity;
oK per Wm-2 of climate forcing
o = for fixed absolute humidity = 0.25 oK/(Wm-2)
RH = for fixed relative humidity = 0.50 oK/(Wm-2)
2 1
1
2.0

0.5Wm
K
RH
Q2CO2  4Wm2
gives
1.6C  T  2.7C
(NRC, 1979, still good?)
Ice-Albedo Feedback
• Ice reflects more solar radiation than other surfaces
• As the Earth warms, ice melts in high latitudes and altitudes
• This lowers the albedo of Earth and leads to further warming.
Add Ice-Albedo Feedback to Water Vapor Feedback
2 1
1

0.1
to

0.9
Wm
K
ice
(NRC, 1979 still good)
Add these changes to the basic relative humidity feedback and get
2 1
1
0.6
to
2.4
Wm
K
RH ice
Q2CO2  4Wm2
now gives
1.7C  T  6.7C
as the uncertainty range for the long-term response to CO2 doubling.
2.1C  TRH ice  3.6C
IPCC - 2001gives
1.5C  T  4.5C
NRC - 1979 gave
T  3.0 1.5 C
Conclusions:
• Uncertainties in projections of global warming are closely
related to uncertainties in climate sensitivity to external forcing.
• Official scientific estimates of climate sensitivity have remained
constant for 20 years, but so have the uncertainties in sensitivity,
which are large.
1.5C  T2CO2  4.5C
• Increased efforts to understand the underlying physical processes
behind the key climate feedback processes are needed, and many
are underway.
• For the time being, however, policymaking on climate will need
to be conducted in the presence of large uncertainty about the exact
consequences of greenhouse gas emissions.
Part II:
The Tropics and Climate Sensitivity
1. The net radiative effect of tropical
convective clouds.
2. The Fixed Anvil Temperature
(FAT) Hypothesis.
GMS-5
IR image
Cloud Feedback
The Greenhouse Effect of Clouds:
Clouds absorb all IR radiation and emit like black bodies
at their temperature. Usually they are cold and emit
less energy than clear skies would in their absence.
TClear Sky  TConvecti ve Anvi l  TTropopause Cirrus
Cloud Radiative Effect
Amount by which clouds
affect the energy balance
at the top-of-atmosphere
High Cloud (p<440mb)
in the tropics
is most common over
warmest SST,
or over land.
t>1
9%
22%
10%
Ri = Ricloudy - Riclear
Tropical clouds in the convective
regions can have strongly positive
or negative effects on the top-ofatmosphere energy balance,
depending on their top altitude
and albedo (optical depth).
Ai •Ri
But, their populations tend to
arrange themselves so that their
net effect on the radiation balance
is small
Conceptual Model:
A convective box with upperlevel clouds, and a clear box.
R1
R2
M
Connect the two with a large-scale
mass flux, M.
Assume that the albedo of the
convective cloud is proportional to
the strength of the mass flux, and
keep the emission temperature of
the convective clouds fixed.
Make the mass flux proportional to
the difference in SST between the
two boxes T = T1 - T2.
Convective
Clear
M
T1
T2
Solve for the equilibrium using column
energy balance.
R1
M
dT1
M
 R1  c p  e  Exp1
dt
A1
dT
M
c 2  R2  c p  e  Exp2
dt
A2
c
Cloud
Convective
b)

Temperatu re (K)
OLR =150
T1
300
R1
T2
0
2000
T1
T2
Ocean
120
110
100
304
302
Atmosphere
Net Radiatio n (Wm-2)
310
306
Clear
M
130
308
R2
R2
4000
6000
Lambda
90
80
70
60
8000
Hartmann, Moy and Fu, 2001, J. Climate
Net Radiation in convective and
nonconvective regions of the tropics
must be the same if:
•Albedo of convective cloud responds sensitively to
circulation or SST gradients.
•Circulation responds sensitively to SST gradients.
•Column energy export is uniform in domain
of interest.
•Equilibrium conditions hold.
•Then if cloud radiative forcing in non-convective
regions is small, it must be small for convective
clouds also.
Within the warm SST
region, the correlation
between high cloud
amount and net radiation
is small.
Finally, the FAT Hypothesis,
Fixed Anvil Temperatures for All Climates.
This was assumed in previous
‘zero net radiative effect of convective cloud theory’.
Now, I want to argue that tropical anvil clouds appear at
a fixed temperature given by fundamental considerations
of:
• Clausius-Clapeyron definition of
saturation vapor pressure dependence
on temperature.
• Dependence of emissivity of
rotational lines of water vapor on
vapor pressure.
Clear-sky Radiative Cooling and Relaxation:
for tropical climatological conditions
In the tropical atmosphere, and the in the global atmosphere,
radiative cooling approximately balances
heating by latent heat release in convection.
The global mean precipitation rate is about 1 meter per year,
which equals an energy input of about 80 Watts/sq. meter,
Requiring a compensating atmospheric radiative cooling
of about 0.7 ˚K/day, averaged over atmosphere.
Rotational Lines
of Water Vapor
and UpperTropospheric
Cooling
Total Beyond 18.5mm -->
Fact: The radiatively-driven
divergence in the clear regions
is related to the decrease of
water vapor with temperature
following the Clausius-Clapeyron
relation and the consequent
low emissivity of water vapor
at those low temperatures.
Hypothesis: 200 hPa
Convective outflow and
associated large-scale
divergence near 200 hPa
are both associated by
radiatively-driven divergence
in clear skies.
Further Conjecture:
The temperature at which the
radiatively-driven divergence
occurs will always remain the same,
and so will the temperature of
the cloud anvil tops.
Testing the FAT Hypothesis in a model.
Larson and Hartmann (2002a,b) Model Study:
MM5 in doubly periodic domain
a) 16x16 box with uniform SST (297, 299, 301, 303K)
b) 16x160 box with sinusoidal SST
Clouds and circulation are predicted
Cloud interact with radiation
Basically, a radiative-convective model in which the
large-scale circulation is allowed to play a role by dividing
the domain into cloudy (rising) and clear (sinking) regions.
Radiative Cooling
in non-convective
region for SST’s
ranging from
297K to 303K.
From Larson &
Hartmann (2002a).
Cooling profile
moves up in
upper troposphere
with increasing SST.
But what happens
to the temperature
at the top of the
cooling profile?
The temperature of the
200 hPa surface increases
about 13K, while the
surface temperature rises
6K.
The temperature at which
the radiative cooling reaches
-0.5 K/day remains constant
at about 212K.
The temperature at which the
visible optical depth of upper
cloud reaches 0.1 remains
constant at about 200K.
Conclusions:
Net radiation in convective regions should be the same as
that in adjacent non-convective regions of the tropics. Hartmann,
Moy and Fu, J. Climate, 2001. This would mean that the net radiative
effect of tropical convective clouds must remain small.
The favored temperature for tropical anvil cloud tops should
remain approximately constant during climate changes of
reasonable magnitude. FAT Hypothesis. Hartmann and Larson, GRL,
2002.
The emission temperature of the rotational lines of water
vapor should also remain approximately constant during
climate change. Hartmann and Larson, GRL, 2002.
These assertions imply relatively strong positive water
vapor and IR cloud feedback, but small net convective
cloud radiative feedback.
Remaining Questions:
To what extent is what I just said correct?
Will the area occupied by tropical convection change with
climate? If so, how? IRIS?
Will the area, or optical properties of boundary layer
clouds change with climate? Feedback looks negative.
What will happen at the tropical tropopause? Will it get
warmer or colder and what will this mean for climate?
Fin